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Theorem intn3an2d 1375
Description: Introduction of a triple conjunct inside a contradiction. (Contributed by FL, 27-Dec-2007.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Hypothesis
Ref Expression
intn3and.1  |-  ( ph  ->  -.  ps )
Assertion
Ref Expression
intn3an2d  |-  ( ph  ->  -.  ( ch  /\  ps  /\  th ) )

Proof of Theorem intn3an2d
StepHypRef Expression
1 intn3and.1 . 2  |-  ( ph  ->  -.  ps )
2 simp2 1006 . 2  |-  ( ( ch  /\  ps  /\  th )  ->  ps )
31, 2nsyl 124 1  |-  ( ph  ->  -.  ( ch  /\  ps  /\  th ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    /\ w3a 982
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 188  df-an 372  df-3an 984
This theorem is referenced by:  iooelexlt  31729  icccncfext  37705  fourierdlem10  37919  fourierdlem104  38014  cznnring  39577
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